89/88: Difference between revisions

Revision as of 04:14, 11 April 2025

This page presents a novelty topic.

It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex.

Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

Interval information

Ratio

89/88

Subgroup monzo

2.11.89 [-3 -1 1⟩

Size in cents

19.56217¢

Name(s)

missing^?

Color name

89o1u1

FJS name

[math]\displaystyle{ \text{A1}^{89}_{11} }[/math]

Special properties

superparticular,
reduced

Tenney height (log₂ nd)

12.9352

Weil height (log₂ max(n, d))

12.9515

Wilson height (sopfr(nd))

106

Comma size

small

Open this interval in xen-calc

89/88 is an 89-limit superparticular comma.

For Budjarn Lambeth’s idiosyncratic uses for this comma, see User:BudjarnLambeth/Tailwind comma.

@@ Line 2: / Line 2: @@
 {{Infobox Interval
-| Name = tailwind comma
 | Color name = 89o1u1
 | Comma = yes
 }}
-'''89/88''', a.k.a. the '''tailwind comma''', is an [[89-limit]] [[superparticular]] [[comma]] tempered out by two of the [[Batch 89 temperaments]].
+'''89/88''' is an [[89-limit]] [[superparticular]] [[comma]].
-Tempering this comma on its own gives the tailwind temperament, a [[rank-2]] 2.11.89 [[subgroup]] temperament.
+For [[Budjarn Lambeth]]’s idiosyncratic uses for this comma, see [[User:BudjarnLambeth/Tailwind comma]].
-Tempering out 89/88 equates the harmonics [[11/8]] and [[89/64]].
+[[Category:Unnamed commas]]
-If ''not'' tempered out, then 89/88 is very well approximated by 1 step of [[36edf]].
-== Tailwind ==
-<pre>
-Equal Temperament Mappings
-	11	89
-[ ⟨	2	7	13	]
-⟨	9	31	58	] ⟩
-Reduced Mapping
-	11	89
-[ ⟨	1	4	7	]
-⟨	0	-1	-1	] ⟩
-TE Generator Tunings (cents)
-⟨1200.9330, 648.6921]
-TE Step Tunings (cents)
-⟨166.43584, 96.45125]
-TE Tuning Map (cents)
-⟨1200.933, 4155.040, 7757.839]
-TE Mistunings (cents)
-⟨0.933, 3.722, -13.041]
-These calculations use inharmonic TE. Subgroup TE will not work because the basis is not a subgroup of the rational numbers or has a redundant entry or something else is wrong.
-Complexity	0.118010
-Adjusted Error	9.221690 cents
-TE Error	1.424038 cents/octave
-Unison Vector
-[-3, -1, 1⟩ (89:88)
-Scala Files
-Number of notes per octave
-TE	2	9
-Pure octaves	2	9
-</pre>
-[[Category:Commas named for other reasons]]

89/88: Difference between revisions

Revision as of 04:14, 11 April 2025

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